On Bank holiday Monday afternoon in a wide, tree- lined road in north London residents are unpacking tennis rackets from cars, returning from parks with children, playing an unthreatening game of dad/son football in the street. The large wisteria-clad houses are displaying Labour stickers. The area is both wealthy and slightly scruffy at the far ends, with some surviving multiple occupancy and social housing. It is what used to count as comfortably well- off in London before the arrival of 1 Hyde Park and the sonic boom in luxury homes.

This is the road where Ed Miliband lives with his lawyer wife Justine and their two small sons. His holiday weekend has been spent working on election strategy, appearing on Andrew Marr and flying paper aeroplanes with his boys at Primrose Hill. Justine, very pretty and animated, has been putting campaign leaflets through doors with their sons, aged three and four. She says: “The children haven’t yet connected the Labour Party with Ed. I think they think everybody’s parents are on TV.” It is not an unreasonable assumption to make in this area of north London.

Inside, the house is warmly assembled rather than interior designed. Ed Miliband poses for our photograph, mildly fretting that he knows his wife dislikes the chair he is sitting in but they have not got round to replacing it.

It looks a cheerful home for busy parents. There are family photographs everywhere, fading lilies in a vase, a cricket ball and miscellaneous clutter in a bowl, shelves of books including Philip Larkin’s poems as well as political tracts. The middle-class soundtrack to our conversation is a gurgling coffee machine. The Labour leader is wearing a blue shirt that appears fresh from its wrapper and chino trousers. He is fighting David Cameron on every front now, including on smart/casual. He says he is not embarking on the usual campaign fitness regime but is slender and unlined at 44.

It is the London housing market which is preoccupying Ed Miliband, who today launches his local and European election campaign with a warning about the capital’s housing crisis.

The Labour leader has taken on press barons, energy giants, bankers, American pharmaceutical companies, and now he is set on foreign housing investors and “buy to leave” stock. To his critics, he is following a Marxist agenda of massive state intervention into the private sector. To his admirers, he is David to Goliath, making a series of principled stands against the over- mighty. His kind of political philosophy has recently gained support from an unexpectedly popular quarter: the fashionable French economist Thomas Piketty states in his best-selling book Capital in the Twenty-First Century that global inequality must be corrected by ferocious taxing of capital.

Miliband confesses: “I’m in the early stages of the book. In a way, he is symptomatic of what people are actually feeling. It doesn’t need Thomas Piketty to tell me that is what people are saying on doorsteps.”

Ed, Justine and their two sons, Daniel and Samuel

Miliband says that he is sticking at a 50 per cent top income tax rate, but that his party does support constraints on capital such as the “mansion tax” on houses worth more than £2 million. We note, but don’t point out, that the house where we are sitting would surely fall within this policy, so for him the politics is personal. “I think even the people who have done well out of the London housing market worry about what happens to their kids. Even the winners from London’s housing market would recognise there are big flaws, that supply is just not keeping up with demand.”

Inequality is the battle standard under which Miliband will fight the general election and he begins in London today. So does he see the top-end prices of 1 Hyde Park or the Battersea power station development as an opportunity or a threat to the capital?

“I think London is an incredibly exciting, brilliant city. But there are big dangers of people being priced out of the housing market, not being paid enough to live on or indeed to live in London. We’ve got to stop this phenomenon of empty properties being bought by overseas investors and nothing done about it. We also have to build more, and that is about everything from use- or-lose-it powers in relation to developers.”

Developers, on the other hand, often blame the slow planning process for holding up new building. “They would say that, wouldn’t they?” says Miliband scornfully. “Look, often you have developers sitting on land and not doing anything because they know the price will go up. But, you know, when I think about the prospect of becoming Prime Minister next year, housing is one of the absolute priorities because it is a crisis. For Generation Rent, for the younger generation, for families who are increasingly living in private rented accommodation, there is a housing crisis.”

Does he believe that London is becoming a city only for rich people? “I think it is increasingly becoming that way, that’s the danger. It is not inevitable.”

How do you buck the market? Miliband’s larger mission is to reform it. “Look, my vision is that markets need rules. Rules which mean they work in the public interest and for ordinary families. Top business people I speak to, and this is different from 10 years ago, say, ‘I’m really worried about inequality’. They may not all agree with my solutions but they really worry about the growing gap, not just the gap between rich and poor, but the rich and everyone else.

“I have this ugly phrase, pre-distribution. It says you’ve got to make sure that when it comes to your economy, even before you get to taxation and benefits, it’s working in a fairer way.”

Miliband may have captured the anxious public mood now on the cost of living, but what happens if the sunshine of economic growth cheers the voters in time for the election? “I welcome any growth there is. But this is the mistake the Tories are making, Osborne, Cameron and Boris Johnson. They don’t get the scale and the depths of the crisis. That is partly what Nigel Farage is tapping into, a sense of deep discontent: is our country run just for the few or the many?”

As Ed Miliband limbers up for a year of campaigning, he is clear about whom he is fighting for and against: against vested interests, for the little guy. Where do the unions fit into this? Miliband believes he has proved his credentials on pushing through union voting reform but he still became party leader because of the union vote and he has been reluctant to criticise the RMT union during the tube strike.

He says that it was wrong for the strike to happen but is critical of the Mayor, Boris Johnson, for its late resolution. “I think the Mayor should have got around the table, I think there is a real issue that the Mayor was not engaging with the Tube workers early on.”

He is also sceptical about the proposed minimum threshold reforms on holding strikes. “I’m personally not convinced of the case for it. I think a better way forward is to say, look, let’s build good relations. Let me make a point on this: we have elections and we don’t have a threshold for turnout for elections. There are other ways to build good relations.”

Is he too close to the unions? “No. Part of being a democratic country is having effective trade unions. Trade unions have an important role in standing up for working people.”

The splashiest news about the Labour election campaign so far has been the hiring of President Obama’s election strategist David Axelrod. Then it turned out that Axelrod would be based in America, so may be more an honorary campaigner. Miliband says this misunderstands Axelrod’s role. He is there primarily for ideas, particularly the great theme of inequality. “I’m proud to have him on the team because of what he believes and what he thinks the challenge is for Britain.”

How will he tackle the “negatives” about Miliband, particularly the allegations that he is personally “weird”? Miliband darkens. “Have they decided that? I think the Tories are very unclear how they are to attack me. Half the time they say it is “back to the Seventies”. Half the time they say, “He doesn’t seem to stand for anything”.

What’s interesting is that of the two leaders in this who could be Prime Minister, between myself and David Cameron, I feel I am the one with much more intellectual self-confidence, actually.”

He becomes impassioned. “I’m not the guy who says, ‘Oh I just want to be Prime Minister because it is a place to reach’. I actually have strong beliefs about how to change the country. This is an incredibly powerful weapon. If you think about what sustains me — and it is not the easiest job in the world being leader of the opposition — what sustained me over three-and-a-half years is that sense of deep conviction.

“I look at David Cameron across the dispatch box and I think to myself, I’m the one with the intellectual self-confidence because I actually know what I believe and I don’t need Lynton Crosby to tell me.” He says Cameron is avoiding election TV debates because “he obviously doesn’t have the confidence”.

Ed Miliband’s self-belief is profound. It is the reason he gives for standing against his brother David for the leadership in an act still offputting for voters. “I’ve always said to Justine, there’s no point going for this if it’s not about something deep and I feel I have got something to say that other people are not going to say, including David.”

Where does this sense of unique purpose come from? “I don’t know,” he says, frowning. “I use this phrase ‘you’ve got to be able to walk in the shoes of others’. That’s why I like elections. Part of the capacity of being a good leader is the capacity to learn from people. What people don’t like is a lack of empathy.”

Ed Miliband’s indomitable sense of personal conviction has carried him from his political victory over his brother in 2010 to the prospect of being Prime Minister in May 2015. Does he feel that the prize is now within reach? He says carefully: “Justine is very good. If ever I thought about things like that she is a very good corrective. Her view has always been, ‘Focus on the task ahead’. We know it is going to be a tough year but I’m relishing it in terms of the fight and the big argument about the country.”

What has he found the toughest part of his political journey so far? “Debating David Cameron will definitely be easier than debating my brother,” he smiles ruefully. “You know what I mean? That was a tough leadership election.”

His campaign strategy will be the politics of the high street, engaging with as many people as he can. He has already spent two days at a hospital in Watford. While Cameron and Osborne show up at big infrastructure projects in hard hats, signalling economic growth, Miliband will be walking in the shoes of others until the soles are worn out.